Multivariate analysis in vector time series

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed

MULTIVARIATE ANALYSIS IN VECTOR TIME SERIES

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.

Relating Agulhas leakage to the Agulhas Current retroflection location

The relation between the Agulhas Current retroflection location and the magnitude of Agulhas leakage, the transport of water from the Indian to the Atlantic Ocean, is investigated in a high-resolution numerical ocean model. Sudden eastward retreats of the Agulhas Current retroflection loop are linearly related to the shedding of Agulhas rings, where larger retreats generate larger rings. Using numerical Lagrangian floats a 37 year time series of the magnitude of Agulhas leakage in the model is constructed. The time series exhibits large amounts of variability, both on weekly and annual time scales. A linear relation is found between the magnitude of Agulhas leakage and the location of the Agulhas Current retroflection, both binned to three month averages. In the relation, a more westward location of the Agulhas Current retroflection corresponds to an increased transport from the Indian Ocean to the Atlantic Ocean. When this relation is used in a linear regression and applied to almost 20 years of altimetry data, it yields a best estimate of the mean magnitude of Agulhas leakage of 13.2 Sv. The early retroflection of 2000, when Agulhas leakage was probably halved, can be identified using the regression

Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1

We analyze the variability in the X-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the over-all second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear andnonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.Comment: 15 pages, to appear in Phys. Rev.

The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors

A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for U. S. time series 1871-1986: versions using real interest rate data, aggregate real consumption data, and return variance data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.

Is There Really an Inverted U-shaped Relation Between Competition and R&D?

We test whether predictions of the Aghion and Howitt (2004) model are supported by firm level data. In particular, we analyze if there is an inverted U-shaped relation between competition and R&D. Results show that the inverted U-shaped relation is supported by the Herfindahl index but not by the price cost margin. Using the Herfindahl index results suggest that breaking up monopolies increases R&D while further increases in competition most likely leads to reduced R&D. Comparing different estimators, we find that time-series based estimators typically result in less clear-cut results, probably driven by a lack of time series variation in measures of competition.R&D; competition; firm size; spillovers

Is There Really an Inverted U-shaped Relation Between Competition and R&D?

We test whether predictions of the Aghion and Howitt (2004) model are supported by firm level data. In particular, we analyze if there is an inverted U-shaped relation between competition and R&D. Results show that the inverted U-shaped relation is supported by the Herfindahl index but not by the price cost margin. Using the Herfindahl index results suggest that breaking up monopolies increases R&D while further increases in competition most likely leads to reduced R&D. Comparing different estimators, we find that time-series based estimators typically result in less clear-cut results, probably driven by a lack of time series variation in measures of competition.R&D; Competition; Firm size; Spillovers